Bearing Operating Principle - FSB Online · Contents 1. Foreword 1 2. Bearing operating principle 2 2.1. The task of a bearing 2 2.2. The hydrodynamic operation of the bearing (fluid

Miba Gle i t lager AG

Ultimate Performance and Durability

BearingOperating Principle

Lagerfunktion Titel ENGLISCH 05.12.2000 15:53 Uhr Seite 5

Contents

1. Foreword 1

2. Bearing operating principle 2

2.1. The task of a bearing 2

2.2. The hydrodynamic operation of the bearing (fluid friction) 4

3. Engine bearings 6

3.1. Bearing locations and their design 6

3.2. Bearing interference fit and stresses 8

3.3. Load behavior 9

3.4. Pin orbital path 11

3.5. Elastohydrodynamic lubricant film computation 12

3.6. Factors determining service life 14

3.7. Accompanying field studies 15

4. Questionnaire on engine data for bearing

4. evaluation 17


1. ForewordHistorically seen, the bearing is a very old machine element

that was already used in antiquity. Leonardo da Vinci identi-

fied and formulated the first laws of friction. Today bearings

are very widespread, particularly due to their use in piston

engines. Nonetheless, because of its complex operation

especially in the reciprocating engine, the bearing continues

to resist exact analytical examination.

This report presents the fundamentals of bearing functionality

and associates these with the possibilities for the operatio-

nally secure design of bearings for the reciprocating engine.

1

Lagerf. S 01-02,19-20 ENGLISCH 05.12.2000 15:38 Uhr Seite 1

2

2. Bearing operatingprinciple

2.1. The task of a bearing

The task of the bearing is to transform directional motion into

rotational motion. This leads to direct contact between the pin

and the bearing and causes friction, which in turn causes heat

and wear. In order to meet the requirements of operational

security, low friction and long lifetime, friction must be reduced

by lubrication. The ideal is achieved when the bearing running

surface and the pin surface are kept fully separated by a lubri-

cating film. In this case friction amounts to only a fraction of

that for direct contact between bearing and pin without lubri-

cation. However, even this significantly reduced friction gene-

rates heat. As long as this heat can be dissipated, the lubrica-

ting film is completely maintained and the bearing material

can handle the loads that occur, the requirement of operatio-

nal security can be met. The interrelationships of the various

friction states in the bearing are depicted in Figure 1 using the

Stribeck curve.


3

Figure 1: Stribeck curve, dependency of friction on rotational speed

(constant load)

Transition point (Speed)

Rotational speed in RPM n

Fric

tio

n c

oef

fici

ent

µ

Static friction

has the shaft resting on thebearing.

Mixed friction

involves partial physical con-tact of the bearing and the pinin the presence of lubricatingoil. The peaks of the surfaceroughness of the bearing andthe pin have more or less con-tact depending on the degreeof mixed friction.

Fluid friction

indicates the rotation of theshaft on a fluid. The bearingand the pin are separated bya fluid lubricant.

Lagerf.S03_18ENGLISCH 05.12.2000 15:41 Uhr Seite 3

4

2.2. The hydrodynamic operationof the bearing (fluid friction)

Figure 2: Pressure behavior and the Gümbel circle in a bearing with full lubrication

To minimize power losses, designers of bearings for recipro-

cating engines strive for a state of fluid friction. Related stu-

dies of the physical processes have been conducted by

Reynolds, Sommerfeld, Gümbel and others.

Figure 2 shows the hydrodynamic operation of a bearing. The

space between the shaft and the bearing is called the lubrica-

tion gap and is filled with lubricant. The rotating shaft pulls

lubricant into the diminishing lubricant gap, which induces the

pressure behavior in the lubricant film as depicted in Figure 2.

Due to the localized pressure at the edge of the bearing, the

pressure profile forms in axial direction.

b Bearing width [mm]dL Bearing diameter [mm]dW Shaft diameter [mm]e ExcentricityF Bearing load [N]FD, FV Bearing load portions

caused by rotation andsqueeze effect [N]

h Lubricant film thickness [mm]h0 Minimum lubricant film

thickness [mm]pmax Maximum lubricant film

pressure [MPa]pDmax,pVmax Maximum lubricant film

pressure caused by rotationand squeeze effect [MPa]

β Angular position of h0,relative to FD

δ Angular position of h0

γ Angular position of bearingload F

ωL Angular velocity of bearingωW Angular velocity of shaft

ψ Relative clearance (dL– dW)

dL

MW (ML at n= ∞)

MW (at n= 0)

Gümbel circle

MW

e

e 0=

1 / 2ψ

b

pm

ax

p max

p Dm

ax

p Vmax

h 0

h

e

ML

F

MW

FV β

δ

ωW

γ

FD

ωL

dL

dW


5

The external forces on the lubricant (load from the shaft, etc.)

and the lubricant film pressure form a dynamic balance. If

rotational speed, size and direction of the load are constant, as

in the stationary case, a stable state of the shaft occurs, that

means constant eccentricity e with respect to direction and size.

This excentricity determines the smallest lubricant film thick-

ness h0, which designates the smallest space between the

shaft and the bore. The center of the shaft shifts on variation

of the influencing factors on the near semicircular curve, the

Gümbel circle. At infinitely high rotational speed, the shaft

center (MW) theoretically shifts to the bearing center (ML).

The minimum lubricant film thickness h0 depends on the

dimensions, the rotational speed, the load of the shaft, and the

viscosity of the lubricant as well as on bearing clearance. The

lubricant film becomes thicker with declining load, rising

lubricant viscosity and increasing rotational speed. Due to the

interplay of multiple parameters such as load capacity, tempe-

rature rise due to increased shearing forces in the oil, reduc-

tion of oil throughput and thus the cooling capacity, as well as

reduced tolerance for balance, form and dimensional devia-

tions, changes in bearing clearance ψ cannot be formulated as

a general rule.

The following serve as reference values for the lower clear-

ance limits: for conrod bearings 0,6 ‰ of the shaft diameter

(dW), for main bearings 0,75 ‰. The associated upper clear-

ance limits result from the respective tolerances. If improve-

ments in the bearing situation are to be achieved through

changes in the bearing clearance, these need to be assessed

on a case-by-case basis.


6

3. Engine bearings

3.1. Bearing locations and theirdesign

Using the example of a typical four-stroke diesel engine,

Figure 3 depicts the bearing locations.

Figure 3: Bearing locations in an engine

Thrust washers,gear bearings

Camshaft bearings

Conrod small endbearings

Conrod bigend bearings

Main bearings,flange bearings(main bearing +thrust washer)

Due to the different functionality of the various bearing posi-

tions, different methods of bearing design and interpretation

criteria are used. Figure 4 depicts the typical steps for deter-

mining the installation situation, the bearing parameters and

the bearing type for various bearing locations.


7

Specific unitload x surface

velocity

Dammageaccumu-

lation

Specific unitloadpquer

Bearingassembly

Pin orbitalpath

Elasto-hydrody-namics

Main bearings, conrod big end bearings

Camshaft bearings, conrod small end bearings

Thrust bearings

Figure 4: Bearing locations and their associated computation methods

Figure 5: Method of bearing design and its interpretation criteria

Used bearing evalution methods

Bearingdesign

Gear bearings, statically loaded bearings

The methods used reflect the current state of the art at Miba.

Figure 5 shows interpretation criteria used for the individual

methods. It is important to note that this state of the art con-

tinues to advance and thereby brings improvements in

methods.

Design method

Installation situation

Specific surface load

Specific surface load x circumferential speed

Bearing path

Elastohydrodynamics

Damage accumulation

Interpretation criteria

radial contact pressure,

tangential compressive stress

values from experience

values from experience

minimum lubricant gap,

lubricant film peak pressure,

heating of lubricant,

oil requirements

lubricant gap distribution,

lubricant film pressure distribution,

lubrication clearance fill ratio

mixed friction

service life reduction depending on engine use


8

3.2. Bearing interference fit andstresses

Pretensioning the bearing half-shells in an installed state pro-

vides for a good contact of the bearing back with the housing.

This contact is necessary to prevent the bearing shell from tur-

ning in the housing and to assure heat dissipation through the

bearing shell to the housing.

The circumferential length of the bearing shell is larger by a

factor of the crush height (2 x SN) than the base bore of the

housing; upon installation this stretches the base bore while

elastically reducing the circumferential length of the bearing.

The circumferential pressure in the bearing causes a radial

holding pressure (pr) between the bearing back and the

housing, which provides a friction hold of the bearing in the

housing.

Figure 6: Crush height and installation tension

SN SN

PS PS

d ϕ

pr • µ

prpr

τ

W

σ G

σ L

σL+dσL

pr radial holding pressure [MPa]PS bolt force [N]Sn crush height [mm]W bearing wall thickness [mm]dϕ angle of section cutted outµ friction coefficientσL circumferential pressure in the bearing

[MPa]σG circumferential pressure in the housing

[MPa]τ tangential stress caused by friction [MPa]


9

3.3. Load behavior

The bearing load in an engine for conrod and main bearings

results from the interaction of gas and mass forces. Thus the

direction and magnitude of the bearing force change continu-

ously. The forces on the engine that cause this nonstationary

load are depicted in Figure 7.

Figure 7: Forces on an internal combustion engine

lateral force of piston cylinderpressure

rod force

cylinder pressure

interia force of piston

radial interia forceof conrod

rotating interia force ofconrod

reaction of theconrod pin force

Force onto neighbouringbearing pins

rotating interiaforce of crankthrow

force onto conrod pins

tangential forceonto crankshaft

conrod force includingtranslational interiaforce of conrod

Str

oke

+pgas+pmass

TDC

BDC


10

Figure 10: Polar diagram of the forces for a conrod bearing

Figure 8 shows the typical force behavior for a conrod bea-

ring, applied by magnitude and direction from the center. Due

to the periodic nature of the four-stroke cycle, a closed curve

results. On the curve the respective crankshaft position is

given in degrees. Loads for stationarily loaded bearings can

be computed according to the laws of statics.


11

3.4. Pin orbital path

Figure 9: Pin orbital diagram (pin path) for a conrod big end bearing, relative to

bearing shell

For nonstationarily loaded bearings, the position and magni-

tude of the smallest lubricant film thickness changes due to

the periodically changing forces. Once in every complete

cycle, the resulting path of the pin center ensues; this is called

the pin orbital path and can be computed with relatively little

effort. In our case this method of computation is based on the

Holland-Lang method with the Sommerfeld numbers accord-

ing to Butenschön, and is used for the design of main-,

conrod- and camshaft bearings.

Figure 9 depicts a pin orbital path for a conrod big end

bearing. The pin changes its position not only circumferen-

tially but also radially. As the pin approaches the bearing sur-

face, the pin displaces lubricant from the reduced gap. This

displacement results in a very significantly increased load

capacity of the lubricant film.

Typical values for the smallest lubricant film thickness (h0min)

are 2–5 µm, which is a small percentage of bearing clearance,

and thus also significantly less than the size of many particles

transported by the lubricant.


12

3.5. Elastohydrodynamic lubricantfilm computation

Crush

Oil groove

Oil drilling

Pin circumference

Bearing circumference

Pin

wid

thB

eari

ng

wid

th

Via the numeric solution of the Reynolds differential equation

carried out on the present case, elastohydrodynamics affords

the possibility of incorporating into the computation the

respective rigidity of the bearing housing and special geome-

tric characteristics of the bearing and the pin.

Figure 10 shows a typical housing model (part of conrod) with

installed bearing shells as well as a development drawing of

the bearing and pin.

Figure 10: Model of housing, bearing shells and pin for elastohydrodynamic

lubricant film computation


13

With incorporation of the elastic deformation of the bearing

environment, the lubricant film peak pressure declines in com-

parison to the computation of the orbital path. The smallest

lubricant film thickness declines and often shifts to the edge of

the bearing. The behavior of lubricant film pressure, clearance

fill ratio and lubricant gap height can be studied over the com-

plete cycle in relation to location and time. For the example of

a conrod bearing with asymmetrical load applicaton, Figure 11

shows the three most important results – lubricant film pres-

sure, clearance fill ratio (0.. empty, 1.. full) and lubricant gap

height – shortly after top dead center ignition.

Figure 11: Results of elastohydrodynamic computation

-90-60

-300

3060

9012

0 150 18

0 210 24

0 270

Bearin

g cir

cum

fere

nce

(deg

)

22 0 -22Bearing width (mm)

1200900600300

0

-90-60

-300

3060

9012

0 150 18

0 210 24

0 270

Bearin

g cir

cum

fere

nce

(deg

)

-90-60

-300

3060

9012

0 150 18

0 210 24

0 270

Bearin

g cir

cum

fere

nce

(deg

)


10


1e+0001e-0011e-002

Lubricant film pressure [bar] Clearance fill ratio [0..1] Lubricant gap height [mm]

On the basis of the results above and the results and interpre-

tation criteria in Figure 5, bearing optimization is possible, and

an estimate of remaining service life can be added with the

help of damage accumulation methods.


14

3.6. Factors determining service life

In addition to functionality assessments by means of standard

calculations, service life estimates have become increasingly

important. Figure 12 summarizes the primary influencing

factors.

Figure 12: Factors influencing service life

Influencing factor

Lubricant film pressure

Lubricant film thickness

Cavitation

Corrosion

Soiled oil, old oil

Effect on

fatigue strength

wear, temperature

material removal, disturbance of

hydrodynamic functionality

material removal, disturbance of

hydrodynamic functionality, change in

tribological characteristics

change in tribological characteristics

How these individual factors influence the service life must be

assessed for different engine applications (collective load)

with consideration for the type of bearing used. An exami-

nation can be carried out in accompanying field studies as

described in Section 3.7.


15

3.7. Accompanying field studies

Engine field tests enable a study of the constructive bearing

design and the theoretical bearing design on the basis of

occurring phenomena with respect to the bearing type under

consideration. Reference values for the necessary time periods

are shown in Figure 13.

Figure 13: Engine field tests by the bearing manufacturer

Review of service life

forecast

Long term behaviour

Fatigue strength

Wear

Metallurgical analysisUsed bearing tests forremaining service life

Bearing findings inrelation to service life

Bearing findings inrelation to service life

Bearing examinationafter running in

Enginer start-up approx. 500 hrs 5000 hrs 10000 hrs

Bearing

service life

extrapolation

Analysis ofphenomena

Corrective/supportingmeasures

Relevant toservice life?

Engine running time

Sp

ecia

l b

ea

rin

g

ph

en

om

en

a

yes no


16

In-depth study of the occurring phenomena such as cavitation

or corrosion might be necessary, depending on their rate of

advance.

Special accompanying programs (which are designed differ-

ently for different types of bearings) enable a prediction of

anticipated service life. On the basis of metallurgical studies

and with studies on test rigs, a determination of remaining

service life can be made based on material fatigue and other

factors.


17

Company: Engine:

Contact for inquiries: Tel. No./Ext.:

General informations

Application:

Area of Service:

System (D= Diesel/P= Petrol) (T= two-/F= four-stroke):

Bore: mm Stroke: mm

Cylinder Distance: mm Number:

Construction (L= in-line, V): V-angle: deg

Conrod/crank ratio: Firing order:

Performance

1.) kW at /min (full load) Proportion: %

2.) kW at /min (max. torque) Proportion: %

3.) kW at /min (overload) Proportion: %

4.) kW at /min ( % load) Proportion: %

5.) kW at /min ( % load) Proportion: %

6.) kW at /min (low idle) Proportion: %

7.) kW at /min (high idle) Proportion: %

Oil Type SAE-Classification: Specification:

Temperatur: M= measured or E=estimated:

Engine intake Bearing intake

con. brg. pist. pin brg. main brg.

normal ˚ C ˚ C

max ˚ C ˚ C

at ˚ C ˚ C

Total oil flow (optional) l/min at nominal speed

l/min at idle

4. Questionnaire on enginedata for bearing evaluation


18

2

3

1

Oil pressure (optional) at Engine inlet / after pump

at ˚ C bar at nominal speed ; bar at idle

at ˚ C bar at nominal speed ; bar at idle

Bearing data of conrod bearing

Mechanical Calculation

Housing Diameter: – mm

Bearing Wall Thickness: – mm Width: – mm

Shaft Diameter: – mm

Clearance ‰

Hydrodynamical Calculation

Radial loads (N)

Indicator-(gas load-) table (every ˚ deg crank angle)

(Data (A=assumed, C=calculated, M=measured): )

for performance: 1, (see performance numbers above)

Mass data

translatory: kg (piston + bolt: conrod proportion: )

rotating: kg (conrod proprtion)

Bearing data of main bearing

Mechanical Calculation

Housing Diameter: – mm

Bearing Wall Thickness: – mm Width: – mm

Shaft Diameter: – mm

Clearance ‰

Hydrodynamical Calculation

Lifetime expectation operating hours

Mass data for crank 1 and counter weights

(axial and radical location)

Angle (˚) Distance (mm)No. Mass (kg) Radius (mm) rel. to TDC to Mb./to ref.

Crank mass 1

Counter weight, crank arm, etc. 2



19

Mass data for crank 2 and counter weigths

(axial and radial location)

Angle (˚) Distance (mm)No. Mass (kg) Radius (mm) rel. zu TDC to Mb/to ref.

Crank mass 1



Mass data for crank 3 and counter weigths


Angle (˚) Distance (mm)Nr.: Mass (kg) Radius (mm) rel. zu TDC to Mb/to ref.

Crank mass 1



Mass data formcrank „n“ and counter weights


Angle (˚) Distance (mm)No. Mass (kg) Radius (mm) rel. zu TDC to Mb/to ref.

Crank mass 1



Elastohydrodynamic bearing calculation

In some cases it can be necessary to carry out an elastohydrodynamic bearing

calculation. A checklist for the required additional input data and the costs for

the calculation will be provided on demand.

2

3

1

2

3

1

2

3

1

In order to get a full estimation of the bearing situation, please enclose also the following required infor-mations: Sketch of crankshaft (including center of masses, sense of rotation and firing order), indicator

tables (load tables), several drawings, ...


Notes



Austria

Bearing Group / Headquarters:

Miba Gleitlager AGDr. Mitterbauer Strasse 3A-4663 LaakirchenPhone: +43/7613/2541Fax: +43/7613/2095e-mail: [email protected]://www.miba-at.com


Documents

Bearing Operating Principle - FSB Online · Contents 1. Foreword 1 2. Bearing operating principle 2 2.1. The task of a bearing 2 2.2. The hydrodynamic operation of the bearing (fluid